On Ugly and Not so Ugly Maths

This week I’ve been writing a grant application. This has meant trawling through a pile of literature I wasn’t terribly familiar with. During that trawling I found this piece of rather ugly maths:

with, on the next page
The authors describe the route to these expressions as involving “tedious but straightforward algebraic manipulations”.
I also came across this,
which is altogether prettier.
My application was to apply the second piece of maths to some specific cases, and extend it a bit, and then apply that to an idea published recently, and try to apply that to real data. In practice this probably means turning the second piece of maths into something like the first. This, ladies and gentlemen, is why we hire students and post-docs.

They actually used the word "tedious" in the paper?! That’s excellent! I wish I’d thought of that: "the samples were prepared via much tedious pipetting and then analysed", or something of that nature!